Pointing to a lady, a man said, "The son of her only brother is the brother of my wife." How is the lady related to the man?

Introduction / Context:
This question combines in-law relationships with blood relations. A man talks about a lady, her only brother and the son of that brother, who is described as the brother of his wife. Your task is to connect these people and identify how the lady stands in relation to the man. Such puzzles test your ability to map family structures across two connected families (the man's own family and his wife's family).

Given Data / Assumptions:
- Reference person: a man. - A lady is being pointed out. - The lady has only one brother. - The son of that only brother is the brother of the man's wife. - The wife's brother is the man's brother-in-law. - We assume standard definitions of father-in-law, mother-in-law and so on.

Concept / Approach:
Start by focusing on the phrase the brother of my wife. That person is the wife's brother and belongs to her parental family. We are told that this same person is the son of the lady's only brother. From this, we deduce that the lady's only brother must be the father of the wife and her brother, making him the man's father-in-law. Once we know the identity of the father-in-law, the lady becomes the sister of that father-in-law.

Step-by-Step Solution:
Step 1: Let the man be M and his wife be W. Step 2: The brother of my wife is W's brother (call him B). By definition, B is the son of W's parents. Step 3: The statement says: The son of her only brother is the brother of my wife. Her refers to the lady being pointed at. So B, the wife's brother, is the son of the lady's only brother. Step 4: If B is the son of the lady's only brother, and B is also W's brother, then W must be another child of that same only brother. That is, the lady's only brother is W's father. Step 5: If the lady's only brother is W's father, then that man is M's father-in-law. Step 6: The question asks how the lady is related to M. Since she is the sister of M's father-in-law, she is the sister of his father-in-law.

Verification / Alternative check:
Construct a small tree: Put W's father (F) and W's aunt (the lady) as siblings. F has two children: W and B. From M's perspective, F is father-in-law, W is wife and B is brother-in-law. The lady stands as F's sister. Therefore, her relationship to M is exactly sister of father-in-law. No other close label fits as precisely in standard family terminology.

Why Other Options Are Wrong:
- Sister: For the lady to be M's sister, she would have to share a parent with M directly, which is not indicated. - Mother: The lady is the sister of W's father, not W's mother and not M's mother. - Mother-in-law: The mother-in-law is W's mother. Here the lady is related through W's father, not described as his wife. - Aunt (in generic sense): While she is indeed aunt to W, the specific relationship to M is best described as sister of father-in-law, which is more precise than simply aunt.

Common Pitfalls:
One common error is to jump to the conclusion that the lady must be the man's mother-in-law because she is connected to his wife's family. However, mother-in-law would require her to be W's mother, not her father's sister. Another frequent mistake is to misread her only brother as the man's brother, which derails the logic. Carefully tracking who her refers to and who is whose parent prevents such confusion.

Final Answer:
The lady is the man's sister of father-in-law.